Equivalent Expressions

Equivalent Expressions

1

Warm UpOBJECTIVE: Students will be able to identify when two expressions are equivalent. Language Objective: Students will be able to explain in writing why two expressions are equivalent.

Agenda

2

Evaluate the following expressions.

9x 6

5(x 3)

2x 5y

when x = 2

when x = 4

when x = 6, y = 4

1. 2. 3.

24

35

32

Scaffold


Agenda

3


9x 6

5(x 3)

2x 5y1. 2. 3.

9(2)6

186

5(4 3)

5(7)

2(6)5(4)

122024 35 32

Distributive Property


Agenda

4


5(x 3)2.

5x

35 Distributive Property

53

53

5

x = 44

Press to return

Agenda

5

Harry and Louis are arguing whether the following expressions are equal.

5 x 5x?What do you think? Provide evidence to support your thinking.

5 plus a number is not the same thing as 5 times a number.

If x = 10, then5+10 is not equal to 5(10).

They are not equal!

Launch- A Disagreement

Explore- Which Mathematical Statement is True?

6

Agenda

With your partner, decide which equations are true for all values of x and y.

Part I. Give a written explanation to support your answer.

Part II. a. Pick any number for the variable(s)b. Substitute the number into the equation to prove if it is true. c. Repeat this with a different number.

Example

7

Agenda

If x = 3, this is not true.

The left expression equals 19.

The right expression equals 33.

This is not true because you are multiplying by four then adding.

On the right side you are just multiplying.

Example:

4x 7 11x?

4x 711x

4x 7 11x

4(3) 7 11(3)

12 7 33

1933

Explore- Which Mathematical Statement is True?

Summary- Which Mathematical Statement is True?

8

Agenda

x x x2?

x x x x 4x

2x 1012x

3xy 3x y

5x 2y 7xy

Click an equation.

3(2x) 6x

?

?

?

?

?

Click to advance to the Practice Activity.

9

Agenda

x x x2

This is not true. The left expression says to add x and x.

The right expression, x2 means to multiply x by x.

If x = 5, this is not true. The left expression will equal 10.

The right expression will equal 25.

x x x 2

55 52

1025

x x x 2

?

Click to Return


10

Agenda

x x x x 4xThis is true. The left expression says to add x four times, which is the same as multiplying x by 4. Repeated addition.

If x = 3, this is true. The left expression will equal 12.


?

x x x x 4x

12 12

3 3 3 34(3)

x x x x 4xClick to Return


11

Agenda

2x 1012xThis is not true. The left expression says to multiply by 2 then add 10. The right expression says to just multiply by 12.

If x = 4, this is not true. The left expression will equal 18.


?

2x 1012x

2x 1012x

2(4)10 12(4)

81048

1848Click to Return


12

Agenda

3xy 3x yThis is not true. The left expression says to multiply the 3, x and y. The right expression says to just multiply by 3 and then add the y.

If x = 2 and y = 5, this is not true. The left expression will equal 30.The right expression will equal 11.

?

3xy 3x y

3xy 3x y

3(2)(5) 3(2)5

3065

3011Commutative

Property!

Click to Return


13

Agenda

5x 2y 7xyThis is not true. The left side says to multiply by a number by 5, then multiply another number by 2. The right side says to just multiply by 7, x and y.

If x = 6, y =10 this is not true. The left side will equal 50.

The right side will equal 420.

?

5x 2y 7xy

5x 2y 7xy

5(6)2(10) 7(6)(10)

3020420

50420

Click to Return


14

Agenda

3(2x) 6xThis is true.The left expression says to multiply by 2 first, then multiply by 3. 3 times 2 is 6. The right expression is 6 times the number.

If x = 11, this is true.The left expression will equal 66.The right expression will equal 66.

?

3(2x) 6x

Associative Property!

3(2x) 6x

3(211) 6(11)

(32)116(11)

6116(11)

66 66

Click to Return


Practice- Matching

15

Agenda

Directions: Decide which expressions on the left hand side of the worksheet are equivalent to the expression on the right hand side. Be sure to provide evidence by substituting in ANY value for the variable, x, you choose.

5(4x)

4(x 5)

(34)x

4(x 2)

4(x 1) 3

Equivalent Expressions

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